An Application of Whale Optimization Algorithm for Heterogeneous Vehicle Routing Problem with Soft Time Windows

Abstract

The Whale Optimization Algorithm (WOA) is a metaheuristic algorithm inspired by the hunting behavior of whales, which involves searching for search for prey, encircling prey, and bubble-net attacking. The WOA consists of exploration phase and exploitation phase, aimed at achieving high-quality solutions. This study proposes the application of the WOA method, combined with Local Search (LS) method, named WOA-LS, to solve the Heterogeneous Vehicle Routing Problem with Time Windows (HVRPTW) under soft time window constraints. The problem-solving process includes adjusting the appropriate parameters of the WOA-LS method, such as the number of populations and the number of iterations, using Taguchi orthogonal arrays and analysis of variance (ANOVA). The parameter results are then used to solve the problem and compare the solutions with those obtained by the Tabu Search (TS) method for 56 benchmark problems with different customer locations. The results show that the WOA-LS method outperforms the TS method for 9 of the 56 problems and achieves the same results for 4 problems. The average solution quality of the WOA-LS method is 3.29% higher than that of the TS method, indicating that the proposed method is effective in solving the problem.